sensors

Article

Design, Modeling, and Evaluation of the EddyCurrent Sensor Deeply Implanted in the Human Body

Rajas Prakash Khokle 1,* ID , Karu P. Esselle 1 and Desmond J. Bokor 2

1 School of Engineering, Macquarie University, Sydney 2109, NSW, Australia; Karu.esselle@mq.edu.au2 Faculty of Medicine and Health Sciences, Macquarie University, Sydney 2109, NSW, Australia;

desbok@iinet.net.au* Correspondence: rajasprakash.khokle@gmail.com; Tel.: +61-412-812-052

Received: 19 September 2018; Accepted: 6 November 2018; Published: 11 November 2018

Abstract: Joint replacement surgeries have enabled motion for millions of people suffering fromarthritis or grave injuries. However, over 10% of these surgeries are revision surgeries. We have firstanalyzed the data from the worldwide orthopedic registers and concluded that the micromotion oforthopedic implants is the major reason for revisions. Then, we propose the use of inductive eddycurrent sensors for in vivo micromotion detection of the order of tens of µm. To design and evaluate itscharacteristics, we have developed efficient strategies for the accurate numerical simulation of eddycurrent sensors implanted in the human body. We present the response of the eddy current sensoras a function of its frequency and position based on the robust curve fit analysis. Sensitivity andSensitivity Range parameters are defined for the present context and are evaluated. The proposedsensors are fabricated and tested in the bovine leg.

Keywords: implantable sensor; eddy current sensor; micromotion sensor; orthopedic implants;electromagnetic FEM analysis

1. Introduction

Human locomotion largely depends on the health of the knee joint. The knee joint consists of thelower end of the femur (thigh bone), the upper end of tibia (shin bone) and patella (knee cap). They areprotected by different cartilages, ligaments and tendons. Various thigh and calf muscles attachedto these bones provide the necessary strength and enable motion. To reduce the friction and enablesmooth operation, these bones are covered by a thin synovial membrane that provides lubrication.In a healthy knee, all these parts work in perfect harmony. However, with age, this process startsfailing, and a person’s movement is restricted. Alternatively, if a person has a disease like arthritis orsuffers from injuries and accidents involving the knee, it results in reduced mobility and pain. Some ofthe common features of a damaged knee joint are bone spurs and narrow joint spaces with damagedligaments and cartilage loss. When a disease or injury is in an advanced state, it is not possible to cureit using any medicine or physiotherapy. In such cases, knee replacement or knee arthroplasty is theonly solution. The knee replacement surgery or the Total Knee Arthroplasty /Replacement (TKA orTKR) aim to resurface the damaged knee parts to improve the joint condition that reduces the painand increases the mobility of the person. Similar procedures exist for hip, shoulder, ankle, wrist andelbow joints.

However, these surgeries often require a revision. The ratio of primary surgeries to revisionsurgeries is known as revision burden. Worldwide, over sixteen major countries maintain some formof the orthopedic register. Out of these, Australia [1,2], New Zealand [3], the United Kingdom [4],Portugal [5] and the Netherlands [6] keep an extensive record of all kinds of the surgeries. Table 1 showsthe revision burden for different arthroplastic surgeries. Apart from these, the USA [7], Switzerland [8],

Sensors 2018, 18, 3888; doi:10.3390/s18113888 www.mdpi.com/journal/sensors

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and Belgium [9] report a revision burden of 8.7%, 9.3% and 7.5% for TKA, respectively. Some of theseregisters, especially from Australia, the UK, and New Zealand, also make note of reasons for revision.The reasons for the revision are loosening (28.7%), pain (20.9%), infection (22.4%), instability (6.3%),implant erosion (5.4%), arthrofibrosis (3.8%), fracture (2.6%), misalignment (2.3%) and others (7.6%).To understand these reasons for revision, the process of osseointegration, implant stability and micromotion are discussed next.

Table 1. Number of orthopedic surgeries from the registers of different countries and revision burdenin % for the different joints.

Australia United Kingdom Holland New Zealand Portugal

Hip Primary 440,841 800,683 125,391 110,208 4384Hip Revision 57,819 89,023 16,991 16,251 648Burden % 11.59 10.00 11.93 12.85 12.87Knee Primary 544,075 875,585 116,780 95,821 4110Knee Revision 48,502 54,278 10,360 6739 291Burden % 8.18 5.83 8.14 6.57 6.61Shoulder Primary 29,068 17,300 2077 7305 111Shoulder Revision 3338 2045 203 571 9Burden % 10.30 10.57 8.90 7.24 7.5Ankle Primary 1662 3185 122 1261 17Ankle Revision 376 358 15 179 1Burden % 18.44 10.10 10.94 12.43 5.55Elbow Primary 2738 1639 107 476 66Elbow Revision 536 507 38 81 4Burden % 16.37 23.62 26.20 14.54 5.71

1.1. Osseointegration, Implant Stability, and Micromotion

Osseointegration is the term used to denote an intimate contact between the bone and the metallicimplants. The principles and process of osseointegration are well known and well understood in theliterature [10–13]. After the surgery, the newly formed tissues start occupying the voids and spaces ofthe micro-porous surface of the implant. The cuts and drills in the tibial or femoral bones are repairedby hematoma formation and mesenchymal tissue. These are later replaced by the woven bone tissues.This is followed by the lamellar bone remodelling and the growth of the bone marrow.

There is evidence that the high relative motion between the implant and the host bone leads to theingrowth of the fibrous tissues rather than bone [14]. Thus, the success of good fixation of the implantby osseointegration depends on a stable interface between the implant surface and the bone [15–17].In [18], a study of the stability of femoral components having a non-porous distal stem was done in thecanine model. It was found that the relative micromotion was 34 µm just after the surgery, which isdecreased to 5 µm within a year that indicated extensive bone regrowth and its excellent stability. It wasconcluded that proximally porous uncemented femoral components are crucial in providing the initialstability to the implant. This research led to the development of the porous implants. Furthermore,in [19], a computational model was developed that explored the implant design features that resistedloosening. The finite element analysis of the contact mechanics of the press-fit hip implants also showedthat minimizing the micromotion, especially during the post-operative situation, should provide anadequate stability for the implant to promote the osseointegration [20].

In [21], it was found that the bone ingrowth was inhibited by the intermittent micromotion of theimplants in rabbits. About 20 cycles of 0.5 mm motion were applied once a day. The motion inducesshear strain that causes fibrous tissue formation instead of the bone. In [22], osseointegration underthe bio-mechanical stress–strain and the bone formation and resorption was studied in the beagle dogs.Their investigations showed that the micromotion of less than 30 µm at the bone implant interfacedoes not interfere with the bone growth. In [23], local micromotion measurement on the femoralstem for Total Hip Replacement (THR) is reported. The failure of the cement-less THR is mainly

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attributed to the aseptic loosening and stability of the implants [24,25]. About 150 µm of micromotionhas been considered as the limit for avoiding the fibrous tissue formation and promoting the boneingrowth [23,25]. In [26], micromotion generation as an effect of applied stress and torque on the bone(dental implants) of different densities was studied. It was found that a mean force of 62.7 N showsthe maximum displacement of 71.9 µm.

Thus, the micromotion of the implant, especially during the early stages of recovery,makes osseointegration difficult and gives rise to the implant instability. This, in due course oftime, creates a painful situation for the patient and later warrants a re-surgery.

1.2. Modalities to Measure the Micromotion

In [27], various techniques currently employed to detect the micromotion of the implantare discussed. They are classified into two groups: imaging based and implant integratedsensor based. Imaging techniques include radiography [28], computed tomography [29],Magnetic Resonance Imaging [29,30], and FDG-PET (Fluorodeoxyglucose-Positron EmissionTomography) [31]. Implant integrated sensors involve the use of accelerometers, vibrometry anddifferential variable reluctance transducer (DVRT).

While radiography is a 2D assessment of a 3D process, computed tomography offers betterquantification of osteolysis. MRI is more useful for the evaluation of the periprosthetic tissue (as MRIprovides an excellent soft tissue contrast). FDG-PET is quite cost intensive and provides accuracy onlywhen combined with other modalities. A detailed procedure to obtain the micromotion information inthe lab settings is described in [32]. It utilizes X-ray opaque markers made from tantalum, inserted atspecific locations in the bone followed by the X-ray imaging at regular intervals. Recently, in [33], a newtechnique based on micro computed tomography (micro-CT) and radiopaque markers is proposed toprovide a full field micromotion measurement at the entire bone–implant interface. This study hasbeen performed for the cement-less femoral stem implants in a human cadaver. It had a standarddeviation of 4 µm and accuracy of over 20 µm.

Implant integrated sensors that use accelerometers with vibrometry are described in [34].Well fixed implants show linear behavior, while loosened ones show an acoustic behavior. However,the specificity and sensitivity of vibrometry is estimated to be only 20% higher than the radio graphs.Another contact based system based on the differential variable reluctance transducer (DVRT) hasbeen developed in [35]. In this setup, the commercially available DVRT sensors from Microstrain Inc.(Williston, MA, USA) were used in contact-based configuration. These sensors also had to be calibratedfrequently to account for the frequency dependent hysteresis. Moreover, the electronics for motiondetection was outside the body.

However, these systems cannot be used for a prolonged monitoring of the orthopedic implant.It is not possible to utilize the X-ray techniques as it would mean a visit by the patient to a radiologisteveryday. In addition, the daily radiation dose from these methods would be detrimental to thepatient’s health. The contact based configuration is not suitable for an implantable micromotion sensoras it would mean changing the design of an orthopedic implant, which has been optimized throughyears of research.

Therefore, an implanted sensor that can sense the micromotion of an orthopedic implant remotely(without modifying or touching the implant) can be very useful in reducing the revision surgeries.The holes drilled for positioning the drilling jig on the bone while doing the surgery are left after doingthe procedure. Holes have a diameter of about 3 mm and length of 12 to 15 mm. These holes are quitegood for implanting the proposed micromotion sensor. These holes are drilled at a distance rangingfrom about 3 mm to 15 mm from the surface of the tibial/femoral implant. Therefore, the proposedremote micromotion should have a stand-off range from about 3 mm to 15 mm and resolution of about10 s of micrometers. Keeping in view the non-magnetic and lossy dielectric nature of the human tissue,we propose using inductive eddy current (EC) sensors for this purpose [36]. In [37], authors havediscussed how eddy current sensors can be utilized for motion detection. In this article, we critically

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analyze the problem of micromotion detection of the orthopedic implant and discuss the simulationstrategy, experimental methods and obtained results.

For the displacement measurement, the physical model and an equivalent circuit model of aneddy current loop is shown in Figure 1. The alternating current in the primary coil generates thealternating magnetic field. This induces eddy currents in the metallic target such that the secondarymagnetic field opposes the primary magnetic field. The coil and the target are considered as weaklycoupled primary coil and shorted secondary coil, respectively. This makes the equivalent circuit modelshown in Figure 1b. The primary coil has its own resistance, whereas for induced eddy currentsthat constitute secondary coil in the equivalent circuit, the power dissipation gives rise to its ownsecondary resistance. If the target moves away from the coil, the amount of eddy current induceddecreases therefore the resistance reflected to the primary coil decreases while the inductance increases.This impedance change is utilized for the displacement measurement. The equivalent inductance,resistance and Q factor of the this simple model can be given by the Equations (1)–(3) [38,39]:

Leq = L1 −ω2M2(x)L2

R22 + ω2L2

2, (1)

Req = R1 +ω2M2(x)R2

R22 + ω2L2

2, (2)

Qeq =ωLR

=

ω(

L1 −ω2M2(x)L2

R22 + ω2L2

2

)R1 +

ω2M2(x)R2

R22 + ω2L2

2

. (3)

Here, R1 and L1 are the resistance and self-inductance of the sensor coil depending on the materialand structure of the coil; R2 and L2 are the equivalent resistance and self-inductance of the targetdepending on the eddy current path, conductivity σ and relative permeability µr of the target; and ω

is the exciting angular frequency of the power source, and M is the mutual inductance between thesensor coil and the target that depends on the relative position x between the sensor and target.

However, these expressions do not account for the dispersive and inhomogeneous nature ofthe human body. In addition, as the angular frequency of operation (ω) increases, the electric fieldstrength also increases as per Maxwell’s equation. In addition, with frequency, the current alongthe loop length varies that further adds to the electric fields. The human body therefore affectsthe operation of such a sensor both by absorbing the power and affecting the sensor characteristics.Furthermore, the loop is printed on a dielectric substrate and has a rectangular cross section which maynot be negligible with respect to the shorter dimension of the loop. Thus, various analytical methodsavailable in literature [40,41] are not suitable for investigating the response of an eddy current sensorimplanted inside the human body. Therefore, full wave analysis by numerical methods is frequentlyemployed [42–45].

Figure 1. (a) physical model and (b) equivalent circuit of the Eddy Current sensor.

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Implanting the sensor inside the human bone at the research stage is both a complicated andexpensive proposition. Furthermore, experimental evaluation alone cannot provide answers to thequestions like the effect of power dissipation and the electromagnetic field distribution in the humantissue, so we setup numerical simulations. Then, we perform analysis in the free space as well as inthe human body with respect to the frequency of operation and stand-off distance. The frequency atwhich the sensor works inside the body without any appreciable change is found out through thesesimulations. Then, the experimental setup is done and the free space results at different stand-offdistances and frequencies are verified. Finally, the experiments with the bovine femur are conductedand the sensor characteristics are evaluated.

2. Methods

2.1. Numerical Modeling of Sensors

Ansys High Frequency Structure Simulator (HFSS) that uses a Finite Element Method to solveMaxwell’s Equations numerically is exclusively used in this study for the numerical modeling of theimplantable eddy current sensor. First, a two-turn loop of length 10 mm and width 2 mm with theline width of 0.2 mm on Rogers 6010 substrate is designed in the XY plane. Then, the tibial bone fromAnsys Human body model is imported as shown in Figure 2a. A rectangular box is defined on thetop side of this tibia (Figure 2b). On boolean subtraction, a flat surface on top of the bone is obtained(Figure 2c). This is equivalent to resurfacing the tibial bone using a power saw during the real TKRprocedure. This surface is thickened to form a thick sheet that has the shape of an orthopedic tibialimplant and Titanium material is assigned to it (Figure 2d). This is followed by drilling cylindricalholes of 3 mm diameter and 15 mm depth in the bone below the orthopedic plate. Then, the eddycurrent sensor loop is inserted below the tibial implant. The orientation of the sensor and the implantis shown in Figure 2e–g. Finally, various muscle tissues from the human body model are imported andthe complete leg is constructed.

Figure 2. (a) model of human tibia from Ansys male body model; (b) a cuboid with 5 mm thicknessintersecting with bone; (c) resurfaced tibial bone obtained by subtracting the cuboid from tibia;(d) placing the tibial orthopedic implant on top of the resurfaced plate; (e) top view showing theeddy current loop with respect to the orthopedic implant. (inset: zoomed-in view of the eddy currentloop); (f) side view showing the distance (D) between the plate and the eddy current loop; (g) completeleg model constructed around the eddy current sensor.

Setting up the correct simulation for the proposed eddy current sensor is a non-trivial task asthe default solver settings do not produce physically correct results (Figure 3a). Since the model willbe simulated at several frequency points at different stand-off distances, it is necessary to ensurethat the simulation produces a converged and physically correct solution with a minimum amountof CPU and RAM consumption. The most important simulation settings that affect the accuracy of

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simulation are convergence criteria, meshing, and the order of the basis functions used. These settingsare evaluated against the memory required, the CPU time and the convergence of the results. To getthe physically viable and correct results, the sensor position is varied along the Z-direction and theimpedance characteristics of the loop are evaluated. The tibial implant is displaced from 0.5 mm to10 mm in steps of 0.5 mm and resistance and inductance are evaluated at 100 MHz.

An eddy current sensor is not used beyond its self resonant frequency (SRF), so we define solutionfrequency as SRF of loop. For determining the SRF, the loop is initially simulated with solutionfrequency of 5.35 GHz, which corresponds to the free space half wavelength perimeter of the loop(56 mm). With this initial simulation, SRF of the loop is found to be 3.3 GHz. For all further simulations,this frequency is used as the solution frequency. Using a smaller solution frequency results in 20% lesssimulation time and 46% less RAM.

It is found that reducing the default convergence criteria to |∆Smax| < 0.001 and 6 s < 0.1 givesslightly smoother curves (Figure 3b). In addition, further tightening of convergence criteria doesnot improve the result despite the increase in the solution time. Hence, order of basis functionand meshing are considered for further improvement. The default setup converges with a lowernumber of mesh elements on the substrate. Consequently, the fields are interpolated at many positions.The interpolation error gives rise to the mesh noise which is found to be more than the reflected fielddue to eddy currents, especially at high stand-off distance. Therefore, to ensure that the field at thepoint of interest is calculated by the solver directly rather than interpolation, and the maximum lengthof any side of tetrahedron on the substrate is limited to 0.5 mm. This setting also has the advantage ofreaching convergence in a low number of passes as the initial mesh is much denser than the automaticmesh generated by the solver.

Figure 3. (a) results from the default solver settings; (b) the effect of setting tighter convergence criteria;(c) the effect of setting tighter convergence criteria along with smaller mesh size for substrate andsecond order basis functions.

Figure 3c shows the smooth variation in resistance and reactance when the second order basisfunctions are used along with the substrate meshing with the maximum tetrahedron length of 0.5 mmand the convergence criteria as |∆Smax| < 0.001 and 6 ∆S < 0.1. From Table 2, it can be seen that theuse of second order basis functions has a clear advantage in terms of number of passes (50% less),number of mesh elements (63% less) and CPU time (37%) required to reach the convergence criteria.However, it consumes 47% more RAM and so the actual simulations are run on a dual socket servermachine with 128 GB RAM.

Table 2. Effect of order of basis function on the system resources. Np—number of passes to reachconvergence criteria.

Order Np Mesh Elements RAM CPU Time (Min:S)

First Order 8 76719 4.81 GB 56:31Second Order 4 28400 7.08 GB 35:52

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2.2. Experimental Setup

The eddy current sensor is fabricated on Rogers 6010 substrate using traditional PCBmanufacturing setup by Lintek Pty. Ltd. at Quenbeyan in New South Wales, Australia. The copperlayers are silver-gold immersion coated for preventing the oxidation. The sensor pads were connectedto the SMA connector using 0.1 mm diameter copper wires of length 10 mm (Figure 4d).

A bovine femur bone bought from the butcher shop is used for studying the effect of the boneand muscle tissue. One end of this bone is cleaved to get a flat surface (Figure 4a). Then, the tissuesurrounding the bone are removed and the bone surface is revealed. Then three holes of diameter3.5 mm are drilled at a distance of 5 mm, 10 mm and 15 mm from the edge of the flat end with a depthof about 20 mm by using a power drill. The holes are drilled in different lines to avoid the effect ofbone–air discontinuity. The bone is aligned in such a way that the titanium implant mounted on themicromotion stage can touch the flat surface of the bone (see Figure 4b). The entire bone is coveredwith a wet towel to avoid the dessication of the bone and the muscle tissues during measurements.It is shown in Figure 4c.

Figure 4. Cow bone preparation for experimental validation. (a) bone cleaved to create a flat surface;(b) placement of bone and titanium implant with the position of three holes (Φ = 3 mm) drilled at3 distances—5 mm, 10 mm and 15 mm; (c) bone covered with the wet towel to avoid dessication;(d) two-turn fabricated inductive sensor connected with an SMA connector with 0.1 mm wires.

To generate the motion of the order of tens of micrometers, a motorized stage is constructedusing a Newport M423 Linear translation stage (Irvine, CA, USA) and a Newport right angled bracket.The stage is driven by Newport TRB25CC actuator integrated with a CONEX CC controller (Irvine,

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CA, USA) and Conex power supply. The controller is connected to the PC to enable the programmingof the motion. To automate the entire measurement process, Agilent PNA-X (Santa Clara, CA, USA) isconnected to the PC via LAN cable. The schematic of the entire setup is shown in the Figure 5.

Figure 5. Schematics of the entire experimental setup in free space showing the micromotion stage,micromotion controller, VNA and PC.

First, the connections to the Conex CC controller via a COM port and to the VNA (AgilentPNA-X N5242A) via LAN port are initialized. Then, the controller state is checked and it is broughtto a zero position by issuing a homing command. This is followed by the calibration of the VNA.The VNA is calibrated by using the open, short and broadband matched loads (Agilent 85052B3.5 mm cal kit). The calibration is quite important in these experiments as the loop that has verylow impedance, especially at a lower frequency, is directly connected to the 50 Ω SMA connectorof VNA. This introduces the mismatch of the order of tens of dBs. Hence, it is necessary to have agood calibration standard in place. However, since the calibration is done until the co-axial cable endpoint and not the SMA connector with wires, their effect is de-embedded by using a two port fixtureremoval tool. The two port results are exported in S2P format. This file is imported into VNA in fixturecorrection tool. This de-embeds the effect of the SMA connector and the 10 mm length wires.

Once the calibration is completed, the target is moved to the end position such that the sensortouches the target. This is taken as zero position. Then, the motion stage is moved by the predeterminedamount and its position is read back and verified. Then, the VNA is triggered with proper settingsfor the frequency range, the number of frequency points, if bandwidth (set to 100 Hz) and thenumber of averaging points (20 points per sample). The point-to-point averaging method is selected.Low IF bandwidth, high averaging and proper calibration and embedding ensure good quality ofthe measurements.

After the measurement is complete, the data is read in a binary block. The results are S-parameters(S11) in dB magnitude and phase form, from which they are converted into impedance (Z) withreal and imaginary parts to extract resistance (R) and inductance (L) of the loop using Equation (4).The motion stage is again activated to go to the next position and the entire ’move–measure–acquire’loop is executed until the motion stage reaches the maximum displacement position:

Z11 =

(S11 + 1S11 − 1

)50 R = <e(Z11) L =

=m(Z11)

2πF. (4)

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3. Results and Analysis

3.1. Numerical and Experimental Results in Free Space

A MATLAB code is written that implements the algorithm mentioned in Section 2.2. The resultsare captured at every 10 MHz increment from 10 MHz to 1.1 GHz. Initially, the sensor is tested in freespace. This is followed by testing in the cow bone at three different distances 5 mm, 10 mm and 15 mm.

The measured and simulated resistance and inductance are compared in Figure 6. The measuredresistance is higher than the simulated resistance. This may be due to the wire resistance or SMAconnector loss that is not accurately modeled by the simulation but dominates the small loop resistanceat lower frequency, which is less than 0.5 Ω. Overall, all of the experimental curves show a behaviorsimilar to that of simulations, especially inductance and the self resonant frequency.

The impedance parameters not only change with the stand-off distance, but they also changewith the frequency as shown in Figure 7. At higher frequencies, the resistance shows higher change inthe resistance with displacement. However, this figure does not give any quantitative measure of thesensitivity or possible range of the sensor. For this purpose, we perform a curve fit analysis and definethe appropriate sensitivity and range parameters (discussed in Section 3.3).

Figure 6. Comparison of simulated and measured resistance and inductance as a function of frequency.

Figure 7. Measured inductance and resistance as a function of stand-off distance and frequency.

3.2. Experiments in a Cow Bone

The femur bone from a cow is prepared as explained in the previous sections. The stand-offdistance has a tolerance of ±0.25 mm due to the human errors. The sensor is inserted in these holesand the motion in 10 µm steps is provided by the micromotion stage. Figure 8 shows the effect of thebone on the impedance characteristics of the EC sensor. Compared to the free space, the self resonant

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frequency of the sensor decreases from 1.14 GHz to 0.52 GHz. Furthermore, since the resistanceincreases, the peak Q factor decreases from 97.7 to 28.8. In addition, the frequency at which the Qfactor peaks decreases from 0.44 GHz to 0.04 GHz.

Figure 8. Comparison of the free space and in body impedance properties of the two-turn eddycurrent sensor.

The impedance parameters of the loop as a function of the displacement of the target at 40 MHzfrequency are plotted in Figure 9. Resistance sensitivity is higher than the inductance sensitivity.With an increase in the stand off distance, the sensitivities for both the resistance and inductancedecrease. However, the decrease in the inductance sensitivity is less than the decrease in theresistance sensitivity.

Figure 9. Change in inductance, resistance and Q Factor with 10 µm motion of the implant at stand offdistance of 5 mm, 10 mm and 15 mm.

3.3. Evaluation of the Sensitivity of EC Sensor

The inductance (L), resistance (R), and the Q-factor changes nonlinearly with the stand-off distance(see Figure 3c). The dependence of R, L and Q factor parameters on distance can be curve fitted usingEquation (5), where y can be resistance, inductance or Q factor, x is the stand-off distance and a, b,and c are co-efficients of the curve fit:

y = axb + c. (5)

For inductance and Q factor, c will be a positive value, whereas a and b will be negative.For resistance, a and c will be positive, whereas b will be negative. This is taken into accountwhile writing a program for curve fit. Thus, for inductance, the equation used is y = c− ax−b and,for resistance, the equation used is y = ax−b + c. Consequently, all of the coefficients are calculatedpositive by curve fit algorithm. This facilitates log–log plot of the values. The result of the curve fit forinductance, resistance and Q factor are shown in Figure 10. The following observations can be madefrom the curve fit analysis.

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1. The curve fit at maximum frequency points is exceptionally good as seen from adjusted R2 graphwhere its value is near to 1.

2. At FSRF, the adjusted R2 drops to a low value for the three parameters. This indicates a failedcurve fit. Correspondingly, the curve fit coefficients have discontinuity or abrupt change at FSRFand so are not reliable indicators of the actual behavior. This behavior is expected as the resistancebecomes infinite and the reactance abruptly changes to negative value; therefore, there are nocurrent flows through the loop and thus the curve fit fails.

3. The adjusted R2 drops at a certain frequency before SRF for resistance (and so the Q factor).It is around 160 MHz. This also indicates that curve fit does not reproduce the data points well.In addition, it can be noted that at this frequency (FWorst), co-efficient a becomes negative forresistance. Co-efficient c always remains positive which merely indicates that the resistanceis positive.

(a) (b)

Figure 10. Curve fit coefficients for inductance (a) and resistance (b).

To investigate this issue of bad curve fit around FWorst = 160 MHz, the resistance–distancecurves are plotted for three different frequencies, at f1 < FWorst, FWorst and f2 > FWorst in Figure 11.At lower frequency f1, the resistance decreases with increasing distance. At f2, the resistance increaseswith distance. FWorst is the transition frequency. Around this frequency, the resistance change is notwell behaved. Therefore, the curve fit of the power law form fails at this frequency. Consequently,operating the sensor around this frequency is not recommended. At higher frequencies, the sensormay be operated and possibly with higher sensitivity but also with higher losses in body as well asloop. To investigate this further, the electric field distribution is shown in Figure 12. It can be seen that,at higher frequency, E fields are much stronger and have a wide distribution in the bone and muscletissue, whereas, at 30 MHz, it is negligible and localized close to the sensor. Therefore, from the pointof view of power dissipation in human body, it is better to operate around 20–30 MHz region.

Figure 11. Resistance–distance curves at three frequencies F1 < FWorst, FWorst and F2 > FWorst showingthe reversal of trend in eddy current sensor at FWorst.

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Figure 12. Distribution of E fields in body at (a) 1 GHz; (b) 30 MHz.

3.4. Definition of EC Sensor Parameters

The curve fit coefficients do not yield any substantial information by themselves. However,they can be used to calculate the output (R, L or Q factor) at any distance. This is used to define usefulsensor parameters. First, the sensitivity is defined as the change in the output quantity y (inductance,resistance, Q Factor) for the 10 µm displacement of the target expressed in logarithmic scale (to thebase 10) by Equation (6):

S10µm(dB) = 10log(

∆yy

). (6)

The logarithmic scale is used to handle very small numbers and produce meaningful graphs.According to this definition, sensitivity of 10 dB means 1 part in 10 is changed for 10 µm motion, 20 dBcorresponds to 1/100, 30 dB to 1/1000 and so on.

Using Equation (6), the sensitivity of the sensor with respect to inductance, resistance and Q factoris calculated at different frequencies between 1 MHz and FSRF and stand-off distances between 1 mmto 20 mm. To facilitate the comparison, the simulated and measured results of the sensitivity analysis isplotted in Figure 13. The colors represent the sensitivity in the dB value. The sensitivity decreases withthe stand-off distance and increases with the frequency as expected. Especially, inductance sensitivityshows this behavior strikingly well. The resistance (and Q factor) sensitivity shows a drop at FWorstfrequency as explained above. However, due to this phenomenon, there is an optimal frequency ofoperation between 1 MHz and FWorst where sensitivity peaks (at 20 MHz).

Based on the definition in Equation (6), sensitivity range is defined at x dB. This is the range atwhich the sensor can detect 10 µm displacement if the detection circuit can produce measurable outputfor x dB change. If the sensor is placed beyond this range, it cannot be used to detect the 10 µm motion.Therefore, the maximum range that a sensor can have for a given level of sensitivity, called sensitivityrange, is plotted in Figure 14.

The simulated and measured results match very closely. However, the measured results showmore sensitivity especially at higher distances than the simulated case. This may be due to theextra length of the rectangular loop created by the wires connecting SMA to the sensor head.Although de-embedding adjusts inductance and resistance and fixes the SRF of the sensor, it cannotprevent the EM fields generated by the extra wires. This issue can be rectified once the completeintegrated circuit for measurement is developed. The agreement of the results, especially the FBest andFWorst frequencies, validate the numerical simulations.

It should be noted that Q factor is the quantity derived mathematically from resistance andinductance measurements. Therefore, if the inductance and resistance could not be measured at agiven distance, the Q factor cannot be calculated as well. However, if they can be measured, then Qfactor can give higher resolution or sensitivity. The increased Q factor sensitivity range, therefore,is merely representative of increases sensitivity and not the actual distance at which the devicecan work.

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Figure 13. Comparison of simulated and measured sensitivities for inductance, resistance and Q factor.

Figure 14. Comparison of simulated and measured sensitivity ranges for inductance, resistance andQ-factor for 10 µm displacement.

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4. Future Directions

The work presented in this article confirms the feasibility of utilizing an eddy current sensor fordetecting the micromotion of the orthopedic implant. Future research involves determining the biocompatible encapsulation for the sensor. Since the bio-compatible material will be in close proximityof the sensor, its effect on the Electromagnetic field distribution must be investigated thoroughly.Furthermore, its effect on the sensitivity and range of the sensor will have to be evaluated. To providethe energy to the sensor and for communication with the external interrogator, a miniaturized boneimplantable antenna has to be designed and tested [46].

5. Conclusions

A numerical model of an eddy current sensor implanted in the tibial bone of the human kneeis created. Then, the reliable and correct simulation settings were determined and validated byexperiments. It is seen that implanting the sensor inside the bone decreases the self resonant frequencyof the sensor as well as sensitivity. A new definition of sensitivity is proposed, based on the curve fitanalysis, that measures the amount of impedance change with stand-off distance and frequency for10 µm change in the position of the orthopaedic implant. It is found that the frequencies in the rangeof 10 MHz to 40 MHz are most suitable considering maximum sensitivity and low power dissipationin the surrounding tissue. The maximum possible stand-off distance for a given sensitivity level is alsocalculated. These results are expected to be useful for an integrated circuit designer who can design alow power circuit for creating a completely standalone implantable sensor. The proposed sensor isdesigned, fabricated and tested in a bovine leg to demonstrate the feasibility of the design.

Author Contributions: D.J.B. identified the need of having an implantable sensor to detect the micromotion ofthe implant. R.P.K. conceived the sensor, conducted the experiments and performed the curve fit analysis. K.P.E.supervised the project.

Acknowledgments: R.P.K. acknowledges Macquarie University for an International Macquarie Grant for ResearchExcellence. The authors would also like to acknowledge Johnson and Johnson Medical Pty Ltd. t/a DePuy Synthes,North Ryde, NSW, Australia for Support For Research Grant (13335/00).

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:

TKA Total Knee ArthroplastyTKR Total Knee ReplacementEC Eddy Current

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